In this paper we study the a priori error estimates of finite element method for the system of time-dependent Poisson-Nernst-Planck equations, and for the first time, we obtain its optimal error estimates in L ∞ (H 1) and L 2 (H 1) norms, and suboptimal error estimates in L ∞ (L 2) norm, with linear element, and optimal error estimates in L ∞ (L 2) norm with quadratic or higher-order element, for both semi-and fully discrete finite element approximations. Numerical experiments are also given to validate the theoretical results.

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